A finite difference analysis of heat conduction problem in a cylinder terminating in a frustum of a cone is presented. The constriction can be either in vacuum or in a gaseous environment. A fine mesh of 2500 x 800 was used for the construction of the grid such that very small constrictions could be analysed sufficiently accurately. Small constrictions i.e., small contact areas separated by large voids filled with a gas are typical of most practical applications involving contact heat transfer. The result of the finite difference analysis shows that gap conductance is predominant for all the gases considered. Gap-to-solid conductance ratio increases as the cone angle decreases due to the decrease of gap thickness. It also indicates that increase of conductance ratio is less significant at higher constriction angles. Finally, predicted conductance parameters are compared with the experimental results for different interfacial gases and a very good agreement is obtained. (C) 2003 Elsevier Ltd. All rights reserved.